Spring device



Feb. 26, 129.46.

'SPRING DEVIICE Filed July 1. 1943 A. svoBoDA INVENTOR. SMM/4 MBY/W fromm/frs Feb. 26, 1946. A. SVOBODA 2,395,768

SPRING DEVICE Filed-July 1,4 1943 5 Sheets-Sheet 2 j??? l i740 mi INVENTOR. Mu@ gfrbm HTTP/VEKS' J 73M, WSW@ Feb. 26,1946. A. SV OBODA 2,395,768

- I SPRING DEVICE Filed July 1, 1943 5 sheets-sheet 5 g ,505 \--//zdined charaler/Istics g (torque mcreasL/zg) n o Y g N 30 per'ah'na n range ngalar move/nekt gf main .9p/*ingl INVENTOR.

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SPRING DEVICE Filed July' l, 1943 l 5 Sheets-Sheet 4 Hammam staLcal farce on the andi/zg gear IN VEN TOR.

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Feb. 26, 1946. A. svoBoDA 2,395,768

- SPRING DEVICE Filed July 1, 1943 5 Sheets-Sheet 5 INVENTOR.

Swaw@ Afro/M4576 transmitting linkage Patented Feb. 26, 1946 l. UNITED sTATEs PATENT oFFicE f SPRING DEVICE Antonin Svoboda, Forest Hills, N. Y. Application July 1, 1943, Serial No. 493,153

2 claims'.

This invention provides a spring device which applies a constant force over a substantial range of movement, or a force varying in accordance with the predetermined law diierent from the characteristic of the spring.

When any member which is resilient orx elastic (which terms are herein used synonymously) is forcibly deformed from its normal or free condition to a stressed condition within its` elastic limit, it exerts a force whose value depends upon the extent of the deformation. The relation between the force exerted by any resilient member and the extent of deformation of the member is termed the force-deformation characteristic of Vthe member, and may be represented by the formula:

F=f(d) where F is the force and d the deformation of the spring. In the case of ordinary springs, including both metal springs and pneumatic springs, F is ordinarily a linear quantity indicating the force in pounds or other convenient unit exerted by the spring in the direction in which the spring is designed to act, and d is also a linear quantity, measured either in distance units or in angular units, indicating the distance which the working end of the spring has been moved from the position which it would occupy in the normal or free position of thespring. So measured, the forcedeformation characteristic of most springs over their working range is, at least approximately,

where K is constant, that is to say, the force applied by the spring ordinarily increases in direct proportion to the extent of deformation and is, therefore, a variable depending upon the position of the working end of the spring.

Before my invention, there was' not available, so far as I am aware, any spring device for exerting a constant force over a substantial working range. Such a device is achieved in accordance with my invention by combining a resilient vmember with a substantially frictionless forceall the parts of which have such critical relative dimensions that the relation between the movements of the input and output elements of the linkage counterbalances the variation in the force applied by the resilient member, so as to produce a constant force at the output element of the linkage.

My invention contemplates also a spring device including a spring and a substantially frictionless linkage in which the force at the output element of the linkage varies in accordance with a desired predetermined law diiering from the force-deformation characteristic of the spring.

In order that my invention may clearly be un,- derstood, I will describe the specic embodiments of it which are shown in the accompanying drawings, in which:

Fig. 1 is a partly diagrammatic View of a spring device embodying my invention and including a quadratic linkage and a spiral spring;

Fig. 2a, is a side view of a similar device in which a tension spring is substituted for the spi# ral spring of Fig. 1; Fig. 2b is a transverse section of a modied device similar to that shown in Fig. 1 in which a flat torsion spring is substituted for the spiral spring shown in Fig. 1;

Fig. 3 is a diagrammatic side elevation of apparatus for eliminating vibration;

Figs. 4 and 5 are similar views of modified apparatus similar to that shown in Fig. 3;

Fig. 6 is a graph for explaining the operation of the apparatus shown in Fig. 5; j D

Fig. 7 is a graph for explaining the application of the spring device to a landing gear;

Figs. 8a, 80 and 8c are diagrammatic side elevatons showing diierent positions of a landing gear including the spring device; and s Figs. 9a and 9b show the spring device arranged for use as the main spring of a timepiece. Fig. 9a is a transverse section on the axis of the quadratic arm of the linkage, and Fig.Y 9b is a face v1ew.

Fig. 1 shows a spring device embodying my invention and consisting of the combination of a resilient member and a linkage.

The linkage Q shown in Fig. 1 constitutes an important part of my invention and is based upon my discovery that a movement bearing a quadratic relation to another movement may be obtained over a substantial range by means of a very simple linkage consisting of two pivoted arms connected by a bar, in which all parts of the linkage have the critical relative dimensions hereinafter specified.

The linkage shown inv Fig. 1 consists of arms Q20, Q30 pivoted at spaced points QI I, QIZ on a support QlD which constitutes the frame or base of the linkage. The arms Q20 and'Q30 are connected by a bar Q40 which is pivoted to themy at points Q21, Q3l located at diierent distances from the points on which the bars are pivoted. All the pivots have their axes parallel so that all -moving parts of the linkage lie in the same plane or in parallel planes.

'Ihe critical relative dimensions of theparts of i Fig. lhas lthe form Yof a spir 2 the linkage are indicated in Fig.` 1 and are the lengths of the members QIO, Q20, Q30, Q measured between pivot points. They are as follows:

Length of frame Q (QI I-QI2) 1.000 Length of longer arm Q (QII-Q2I) 1.780 Length of shorter arm Q (QI2-Q3I) 1.276

Length of connecting bar Q (Q2I-Q3I) 2.270

As .it is the relationship between the dimensions which is fcritical, the length eof the lframe. Q10 between-the pivot points QII vand Ql2 has, Yfor convenience, been taken as unity so that the gures set opposite the lengths of the other parts express the relation between the length of the frame QIO.

(whichl term the quadratic element) 'rom a xedzeroline Q33'lyingat ,an angle of;2712'14" to .the .line .QH-QIZ of the base Q10, a: 'is the angular distance of the arm Q20 (which I term .the linear element) Yfrom a fixed zero Aline Q23 lying .at an angle of '2621735 from the line QII-Q'IZ of thebase QI'0., and C is a constant .whose value is 1/256 if :x: and y are measured in degrees, .or .02238 if a: and y are measured ,in radians.

'.'Ihe quadratic relationship `between the positions of .the vtwo .arms holds with great exactness over 'the range .of '80 to 150 for the .arm Q20. Within this range, the position of the 'quadratic arm Q30 is always Within plus or minus 40", or less than one-tenth of one per cent., of the position lgiven by the aboveiormula. lThe range may 'be extended trom .60 to 170 Ifor Vthe arm Q20 without 'introducing '.errors 'greater than 3 and these do not seriously affect Vthe operation of the linkage when used as 4part of :my spring device.

To "illustrate, and permt verification of, the quadratic relationship, pointers and'scales or the .two arms graduated in .degrees from `their respective zero lines are shown iin Fig. 1. These lscales do not form.' part of the 'linkage mechanism. y.

'To save Vneedless repetition, vil shall refer tothe linkage which has been described as a quadratic linkage," Vdefining this 4terrn to mean -a linkage having two connected elements whose movements measured from fixed `zero lines bear `an approximately lquadratic relationship to each Vother -over a. `substantial range; and I shall distinguish the two elements as the linear and "fquadratic elements of the linkage.

The resilient member R of the device shown in "l spring exerting a torque around the pivot QI'I of lthe arm Q20, the linear element of the linkage. One end RI of the spring R is anchored to the .frame Yor support Q10 of -the linkage. For reasons hereinater explained, this end .of the spring is 'mounted so A'tirant Hits position'may be adj usted angularly about the pivot-QI I. For this purpose, this end of the spring )is attached 'to -a sector I3 pivoted on the frame Q10 at QI I andadjustable `about its pivot by f. means of a crank EI4 and a shaft I5 which is journalled on the vframe QH) and carries a wor-m I0 engaging gear 'teeth I`1 `on the periphery of the sector I3.

"The other end R2 of the spring R is attached these lengths and n to the arm Q20. When the spring is stressed, the spring exerts a torque on the arm Q20 tending to move it counterclockwise. The position of the end Ri of the spring is such that the spring would be free or unstressed if the arm Q20 lay along the zero line Q23 referred to in the description of the linkage.

The Working range of the spring lies between the position in which the arm Q20 is at 60 to the line Q23 andthe position in which it is at 170 to .the line Q23. Over .this working range, the force-deformation characteristic of the spring Where F is the angular force or torque exerted on the arm Q20, d is the angular distance between the -lineQ33 and the position of the arm Q20, and K is a constant. In other Words, the torque of the spr-ing is directly proportional to the angular deformation of `the spring from .its free position, as `is .usually .the case .with .springs of .this .charf acter.

The .linkage exactly .counterbalances the .forcedeformation characteristic of the spring .so that the angular .force l.or torque which .the .spring through the'linkage applies to the quadratic .element of the linkage, the output arm Q30, .is .substantially constant throughout the working range of the spring, and is accurately constant throughout the range of to 150 for the arm Q20. The reason for this will be explained:

Since the spring is in free or unstressed condition When the arm 4Q20 -is `at the yzero line Q23 .from which the positionxof the arm Q20 is measured as explained in the description of the 1ink age, the angles representing the deformation of the spring and the position of the arm Q20 are identical:

Since the :friction in the pivots :of the linkage may bemadepractically nil, .the law -of :conserva- .tion of energy requires that the torques 'of the arms `.Q20 and Q30 be inversely proportional to `ir-iitiinitesimal incrementsof their movements, :that

is to say,

Frd=Fy-dy (4) Where Fx is the torque applied to the 'arm Q20 "and Fy iis the torque applied to the 1arm Q30. Since the spring acts directly lagainst the armQZ'. FI=F=Kd='K-:c (5) by Equations Zand 3. :Substituting in Equation 4 the value for Fx given in Equation 5 and the value of y given in Equation 1 we obtain 'that is vto say, the output torque Fy is constant. It thus appears that the linkage exactly counterbalances the characteristic of the spring so as to produce 'a constant output torque. 'It Vis evi.-

T rdent Arnathematically that this result occurs because the 'relation ofthe movements of the output and input elements of vthe linkage 'is i/:Cffzw da: '(9) while the characteristic: of the spring -is F=f(d) (10;)

and the spring is so attached to the linkage that rc and d are equal. l

If a spring whose 'force-deformation characteristic differs from that of the spring'R be Vsubstituted for the spring R in the device described, it is possible to obtain a practically constant output torque from the device by making an adjustment inthe position of the sector I3. In the case of any spring whose force is not exactly proportional to its extent of deformation from unstressed position, it has been found that a very close approximation to the actual forces produced by the spring over its Working range can be obtained by considering such forces proportional to the extent of deformation of the spring measured from a slightly stressed condition of the spring. Over the working range of such a spring, the force-deformation characteristic may be expressed by the equation:

where a is a small constant which may be either positive or negative. This formula gives `a Very close approximation to the forces produced by the spring over its working range.

When such a spring is used in the device which has been described, a constant output torque may be obtained on the quadratic arm Q30 by merely adjusting the sector I3 so as to place the unstressed position of the working end R2 of the spring on a line R3 at the angle a from the zero line Q23. The extent of deformation d is then measured from the line R3, but x is measured from the zero line Q23 as before, so that It is apparent that Equations 11 and 12 make Fx equal to K-:z: as before, so that Fy will be a constant.

Other types of springs may be substituted for the spiral spring R shown in Fig 1:

Fig. 2a shows a tension spring R applied to a quadratic linkage like that shown in Fig. 1. The tension spring is anchored at one end to the frame QIO and exerts a tension on a band R4 wound on and attached to a cylindrical drum Q25 which is fixed to the linear arm Q20 so that the spring applies a torque to this arm.

Fig. 2b shows a at torsion spring R2 arranged to apply a torque to the linear arm Q20 of the linkage. One end of the spring is attached to a short shaft QH on which the arm Q20 is fixed, while the other end of the spring is secured to a square shaft R5 which is held against rotation by engagement with a square hole in the frame Q|0.

'I'he modified devices shown in Figs. 2a and 2b operate in the manner which has been described in connection With the device shown in Fig. 1.

In the use of the spring device which has been described, the quadratic arm Q30 is connected to something to which a constant torque or force is to be applied while the frame or base QIO is held stationary; or, if desired, the quadratic arm Q30 may be held stationary and the base Q|0 used to apply the constant torque to a movable member.

The constant-torque spring device which has been described is useful for many purposes, a few of which will be mentioned for the sake of illustration.

The spring device may be used in a construction of an extremely effective device for eliminating vibration. Such a device is shown in Fig. 3.

Fig. 3 shows a spring device which, like that shown in Fig. 1, consists of a quadratic linkage Q and a spiral spring R. The base QID' of the -3 linkage is of a different form from that shown in Fig. 1 and the adjustable sector I3 is omitted. The linear and quadratic arms Q20, Q30 are shown at the middle of their ranges of move-Y ment, instead of near one end of their ranges as in Fig. 1.

An arm 60 is formed integral lwith the quadratic arm Q30 of the linkage and extends at such an angle to that arm as to be horizontal when the arm Q30 is at the middle of its range. At the end of the arm 60 is a cross-piece El whose outer surface lies on an arc whose center is at the pivot Ql2. A massive member 10 is suspended from the arm 60 by a cord or band 1| attached to the upper end of the cross-piece 6| and lying against the arcuate face of this piece. The strength of the spring R is such that the constant torque which it applies to the arm Q30 is exactly equal to the torque applied to this arm in the opposite direction by the force of gravity on the member 10 acting through the arm 60. rIhe mass or'inertia of the member 10 is very much greater than the mass or inertia of the moving parts of the spring device including the linkage.

In the use of the device shown in Fig. 3, the base Q10 is mounted on a member 'l5 which is subjected to vertical vibration. Notwithstanding this vibration, it will be found that the member 10 remains practically stationary. This is 'because the system is in a state of perfect balance so that the forces caused by the vertical acceleration and deceleration of the base Q|0 result in movements of the spring device and its linkage, whose inertia is slight, without causing appreciable movement of the member 10 whose inertia is large.

The device may be used as a seismograph in which case the member 15 is the earth and a scale or other means may be provided for observing oscillations cf the arm Q20 or the arm Q30. The device may also be used to protect delicate instruments and the like from the vibration of machines or Vvehicles on which they are carried. In this case, the member I5 is part of the machine or vehicle, While the instrument is the member 'l0 suspended by the cord 1|.

The device of Fig. 3 is in what is known as metastable equilibrium, that is to say, the spring and gravitational torques on the arm Q30 are exactly balanced in all positions of this arm within the working range, so that there is no tendency for the arm Q30 to return to any particular position within its range. This is a disadvantage for some purposes, for the device will cease to operate to eliminate vibration in case irregular shocks drive the arms to one end of their range.

Figs. 4 and 5 show modied devices for eliminating vibration in which stable equilibrium is obtained.

InFig. 4, a coil spring l2 very much weaker than the springR extends between the member l0 and a member I9 secured to the base Q10'. This spring is in unstressed condition when the arm 60 is horizontal and the arms Q20 and Q30 are -at the middle of their ranges of movement. The spring 12 exerts a slight push or pull on the member 'l0 whenever the arms are displaced from the middles 0f their ranges, and thus produces a condition of stable equilibrium. The spring is, however, so weak that the forces which it applies to the member 'l0 on up and down vibration of the frame Q|0 are not suicient to cause appreciable vibration of the heavy member 10.

:torque :applied ztothe arm Q30 from zthe constant to the y"yariable `which `increasesv slightly with increase Yoir. This A:is indicated ,by the dotted lline in the graph pfshown in lFig. v6 in which output torque is plottedragainsttheangularzmovement :v of the .armQZll-.and the working end of the spring. The springtorque on the 'arm Q30 may thus be made slightly .greater `than the -gravitational torque .from-the-weight 10 at vthe outer end of the Working range and slightly less at the inner end of the range, so lthat a condition of stable equilibrium ,is obtained at :an intermediate point where the .spring-torque-is equal to `the 'gravitational torque. Since the -variation :in the Spring torque on the farm Q30 depends upon the size of the small l,

anglete, it maybe accurately adjusted by the fhand-le M :and sector I3 .to be only sufficient to prevent the :arms from reaching the ends of ttheir ranges .of movement during the operation ofithe 1vibration leliminating device.

The .constant-torque spring device may be used as the spring suspension of Aa vehicle to prevent the rebound which :occurs in ordinary spring suspensions. .Such useof the device in an air- `.plane"z-landing gear is shown in Figs. 8a, 8b, 8c. .The `iframe Q102 .-of the spring device is secured :toathe bottomQ of the body of the airplane and a ,stop .-I8 is VAprovided. on the frame to .prevent the .farm Q :from mov-ing, beyond theinner end oi "the working rangeof the :gear .--80 carrying -a wheel 8| is pivoted to vthe frame tgl-02 vof the :spring device at the .point .QI.2 -at which the quadratic arm Q is pivoted. `The .landing gearhas an arm 82 connected to .thearm Q30 through a shock absorber 83.

@It will be seen that in the arrangement de- .scribed .the Vconstant-force spring device and the variable-force spring of the shock absorber 83 areconnected in series betweenthe vehicle'body and .the fwheel. The spring R of the constantforce yspring device `is of such strength that the constant force exerted .by the device to urge the Wheelaway from the body is slightlyygreater-than the normal static .load on the wheel after the airplane is landed. The maximum force which -can be exerted by the spring of the shock ab- -sorberfis at least asgreat as the force exerted by -the constant-.force spring device. Consequently, lwhenthe -Wheelis urged ltowards the body, the y"apprmiching movement .of the wheel toward the fbody is .opposed by the increasing force of the .spring of :the shock absorber 03 until this spring has .been deformed to a, point where -it exerts -a force requal to the force of the constant-force -spring device. Further approaching of the wheel then causes no further deformation of the spring .ofthe vshock-absorber 83, but the constant-force y.spring .device yields, opposing further approach- .ingmovement :bya forceslightlyj greater than the normal static load on the wheel over the Acom- -spring The landing i nsassgrzes ,plete :range of `:movement 'inf the constant-'fierce spring device. Afgraph Aof thezspring'forcefopposing upwardi movement v of :the-Wheel :isshown .inFig 7.. The effect of Yopposingupward move- Vment of the vwheel vby a spring -force ofthe-character shown :in Fig. 7 is to vprovide `forabsorb- 'ingthe shock of landing in the usual manner Iand then :to avoid upward movementy or .bouncing Lof .the airplane if obstructions are encountered by the wheel. The operation .is-illustrated vin Figs. 8a., 8b, -8c.

Fig. .Sashows the position yof the parts just vbefore the wheel 8l strikes the ground. The torsion fspring'R is at the inner lend of itsworking range and is stressed-'suciently to hold the arm Q20 against the stop 18. Thespring of the shock absorber is unstressed.

When the -Wheel fstrikes'the. ground, theeshook *absorber `spring Vyields ias 'shown :in Fig. bgthus 'absorbing the ,shock of landinglin the :usual manner.

Ifithe vwheel 18| "then'strikes an obstruction as Yshown in Fig. 8c, .fur-ther upward movement :of

.the wheel .toward the .body is Vopposed only by l Atheconstant torque of the spiral spring `on lthe .arm Q30. The spring device, thereiorefyields to permit the wheel topass over the obstruction without increasing the down force on the wheel. Consequently, aftertthe wheel isspassed over the obstruction-.it moves downwardly to theposition shown in Fig. 8b under he constant torque of `the fspiral spring on the varm Q30 which, as shown in Fig. 7, slightly exceeds the static load on the wheel. Since no increased iforce is applied between thebody and the :wheel .whenthe wheel is moved up by the obstruction, the bodyof lithe airplane is notrnoved upward to any appreciable extent and there is no bouncing.

As a safety measure to preventthe wheel vfrom moving upwardly against the body in the'zcaseof a bad landing which .places too large aloadzon the landing gear, the upward movement of `the Awheelsislimited at the end of the working 'range of .the spring device by .contact between a stop 86 on the arm Q30y and adamped spring :bumper 81 on an arm -88extending from the iframe G2102.

The constant-torque device may be vused yas themain spring oi a timepiece. Itis recognized that the rate of an accurate timepiece, such .as a chronometer, is varied by a .change in the torque applied to the clockwork by the main spring. To obtain accuracy, vit has 'heretofore been necessary to use a very long main spring and .to wind the spring frequently. With my spring device, greater accuracy can be obtained, las the torque remains constant throughout the working .range 10i .the spring. Furthermore, the

v:case the frame :G2103 of the quadratic .linkage has the form of a gear rotatably mounted onza shaft Ql'22 inwhich the quadratic .armlQSBfofthe :linkage vis fixed. The tremainderco'f the linkage and the .spring Rare arranged as before'.

The shaft QIZZ is journalled on the frame '90 of thezclockwork and may carry fa gearSfl. =Pin ions 92, 93 von shafts journalled on the frame '90 engage the gears'li and QI03.

It will be seen that with this arrangement the constant 'torque which the spring :through the ,linkageeappliesfto the quadratic arm Q30 'tends to 'rotate -itl-1e `.gear .19| in fone vdirection and the gear Ql3 in the opposite direction. Thus either of the pinions 92 or 93 may be used to drive the clockwork while the other may be connected to the ordinary ratchet mechanism and used for Winding the spring.

When Ithe spring device is fully wound, the arm Q3!) engages a stop QIS on the gear QIUS. The device Will then exert a constant torque on the clockwork until the arm Q30 has moved into engagement with the stop QI4. The spring may be rewound at any time before this occurs and the operation of rewinding causes no change in the torque applied to the clockwork.

What I claim is:

l. A linkage mechanism consisting of a frame, two arms pivoted to the frame and a bar connecting the arms and pivoted to each of them in which the lengths of the arms and the bar measured between pivot points bear substantially the following critical relationships to the distance between the two pivot points on the frame:

Longer arm 1.78 Shorter arm 1.28 Connecting bar 2.27

so that, when the longer arm is moved within a range extending between the positions in which it makes angles of 80 and 150 with its Zero line at an angle of about 262 to the line connecting the pivots on the frame, the movement of the shorter arm measured from a fixed zero line closely approximates the square of the movement of the longer arm measured from its aforesaid zero line.

2. A spring device comprising the combination with a linkage as claimed in claim 1 of a spring having one of its ends attached to the frame of the linkage and its other end acting against the longer arm of the linkage and positioned so as to urge said arm towards its zero position and to be substantially free from deformation when said arm is in its zero position.

ANTONIN SVOBODA. 

